Time

T

\(\mathbb {N}\)



35040

number of time steps


M

\(\mathbb {N}\)



12

number of months


ts

\(\mathbb {R}_{+}^{T}\)

s

900^{1}

time steps

PV

N

\(\mathbb {N}\)



4

number of PV configurations


J

\(\mathbb {N}\)



4

number of roof planes


Cf^{pv}

\(\mathbb {R}_{+}\)

CHF

2749

PV fixed cost


C
^{mod}

\(\mathbb {R}_{+}^{N}\)

CHF/W

0.610^{1}

PV configurations, specific costs


\(P^{\textsc {mod}}_{\text {nom}}\)

\(\mathbb {R}_{+}^{N}\)

W

315^{1}

PV unit nominal power


P
^{mod}

\(\mathbb {R}_{+}^{T\times N}\)

W

^{2}

PV configuration unit generation


A
^{mod}

\(\mathbb {R}_{+}^{N}\)

m^{2}

1.631^{1}

PV configuration areas


A
^{roof}

\(\mathbb {R}_{+}^{J}\)

m^{2}

23^{1}

roof planes areas


γ
^{PV}

\(\mathbb {R}\)



0.5%

annual maintenance specific cost


β
_{
i}

[0−90]^{N}

deg

^{3}
 

ω
_{
i}

[0−360]^{N}

deg

^{3}

PV configuration azimuth

Battery

B

\(\mathbb {N}\)



1

number of batteries


soc_{0}

[0,1]^{B}



0.7

initial state of charge


soc_{min}

[0,1]^{B}



0

minimum state of charge


soc_{max}

[0,1]^{B}



0.7

maximum state of charge


α

\(\mathbb {R}_{+}^{B}\)

s
^{−1}

4.63·10^{−7}

battery selfdischarge rate


η
^{cha}

[0,1]^{B}



0.98

battery charging efficiency


η
^{dis}

[0,1]^{B}



0.98

battery discharging efficiency


γ
^{cha}

\(\mathbb {R}_{+}^{B}\)

1/s

1/3600

battery charge C rate


γ
^{dis}

\(\mathbb {R}_{+}^{B}\)

1/s

1/3600

battery discharge C rate


C
^{bat}

\(\mathbb {R}_{+}^{B}\)

CHF/J

5.07·10^{−5}^{4}

battery specific cost


\(C_{F}^{\textsc {bat}}\)

\(\mathbb {R}_{+}^{B}\)

CHF

0

battery fixed cost


\(C_{O}^{\textsc {bat}}\)

\(\mathbb {R}_{+}^{B}\)

CHF/J

0

operational cost of storage

System

L

\(\mathbb {N}\)

years

25

system lifetime


L
^{bat}

\(\mathbb {R}_{+}\)

years

9

expected battery lifetime


r

\(\mathbb {R}\)



1.5%

discount rate
